One of the fundamental questions in quantum field theory in curved spacetime concerns the nature of the vacuum state. This is the subject that we address in this thesis. A generalised Schrödinger wave functional equation is constructed, and a general framework is introduced to solve the Schrödinger equation for a general curved spacetime. Vacuum wave functional solutions are given for a wide class of spacetimes; namely static, dynamic and conformally static. These include the physically important Robertson-Walker, Bianchi type I, de Sitter, Rindler and Schwarzschild spacetimes. The nature of the vacuum state in these spacetimes is extensively discussed. Matrix elements and two-point functions are then calculated in this general framework. This formalism is used to study particle creation and boundary effects on curved spacetime. This is carried out first for cosmological models, which exhibit particle creation as a result of the expansion of the universe. Secondly, quantum field theory from the view point of an accelerating observer is investigated. The Minkowski vacuum state is shown to be a thermal state with respect to the accelerating observers ground state. The application of this formalism to black hole spacetimes is also investigated.